Color Only Non-Planar Faces
I don't think you can get that with standard tools. I would use a script to highlight (select in edit-mode) non coplanar faces:

import bpy
import bmesh

obj = bpy.context.active_object  # Get selected object

if obj:
    bpy.ops.object.mode_set(mode='EDIT')  # Go into edit mode
    bpy.ops.mesh.select_all(action='DESELECT')  # Deselect everything

    bm = bmesh.from_edit_mesh(obj.data)  # Create bmesh object for easy mesh evaluation

    for f in bm.faces:  # Check all the faces
        # 3 points will always define a unique plane. We define its coordinates.
        A = f.verts[0]
        B = f.verts[1]
        C = f.verts[2]
        a1 = B.co.x - A.co.x
        b1 = B.co.y - A.co.y 
        c1 = B.co.z - A.co.z 
        a2 = C.co.x - A.co.x
        b2 = C.co.y - A.co.y
        c2 = C.co.z - A.co.z
        a = b1 * c2 - b2 * c1 
        b = a2 * c1 - a1 * c2 
        c = a1 * b2 - b1 * a2 
        d = (- a * A.co.x - b * A.co.y - c * A.co.z)
        # Check if any point after the third one is a part of this plane (ie the distance to the plane is == 0)
        if len(f.verts) &gt; 3:
            for v in f.verts[3::]:
                if a * v.co.x + b * v.co.y + c * v.co.z + d != 0:
                    f.select_set(True)  # If this vertex is not part of the base plane, select the face and break
                    break

    bmesh.update_edit_mesh(obj.data)


Illustration :



Also, if you want faces to highlight only if the vertices deviate from a certain threshold to to the base plane, you could insert it in the code :

Replace

if a * v.co.x + b * v.co.y + c * v.co.z + d != 0:


With 

if abs(a * v.co.x + b * v.co.y + c * v.co.z + d) &gt; 2 :  # Threshold


Note that this is not deterministic and could change depending on which vertices get evaluated to define the plane coordinates.



Further and further reading.